I'm late to this thread, but I figured I'd chime in about the shy/abused rescue Basenji.
Our Tana has been with us for just over 2 years. She was a puppymill breeding female.
At the beginning, she was very very skittish, timid & anxious. She went from her foster home- a big place where she could hide from anything….to our semi truck. Small space, no hidey-holes. No choice but to learn to accept us. I left her alone for the first couple of weeks- no unnecessary advances, just feeding & walks, calm voices....no coddling, no babying. Just being in each other's presence. I let HER get used to me, see the routine, so she'd learn what we were all about.
Despite her shyness, from day 1 she did always sleep tucked under my arm. She'd lay there half-crouched, licking the sheets (is that like a thumb-sucking behavior?) until she fell asleep.
Her progress was gradual. By two months she seemed to be relaxed around me. By four months, she figured out she could engage me in PLAY...which was clearly a great revelation for her....I could just see the joy in her, for the first time, when she play-bowed and slapped at me and I responded playfully. Before that, she'd only engaged Jibini in play. That may have been the first time she ever initiated play with a human.
By 6-8 months, she began to tolerate Fred, began to show curiosity with strangers & new situations. By one year, she was almost entirely a different dog. I don't know if her progress was normal or unusually fast- but I think being a trucker dog, getting SO MUCH constant socialization, really helped her figure things out quickly.
Over the last year, she has truly come full circle, finally. She still refused to do more than "tolerate" Fred for the longest time....He felt kind of bad, thinking Tana hated him. She did kind of act like he was contagious....she wanted to be as far from him as physically possible. But when we adopted Chloe, suddenly Tana had COMPETITION for attention! And since Chloe absolutely adores the very earth Fred walks on, suddenly Tana became Fred's best friend too!! It is so funny to see this little dog who used to regard Fred like a fart in a car....suddenly scramble to be the first one to cuddle up in his arms so he won't be able to pet Chloe. She is almost FAWNING over him. It's great.
That, and she has FINALLY accepted crating. Until this past October, really, she's been the type to shred, whine and poop in her crate- she became a basket case. I know it's not widely reccomended, but after 2 years together in a semi truck, I was fairly sure Jibini & Tana could be crated in an extra-large crate without trouble. So I started crating them together....for no more than 2-3 hours at a time.
So far, so good...and it has helped Tana's anxiety immensely. I notice now, when it's time for me to go to work, Tana will actually let me come pick her up so I can bring her to the crate. Used to be, I'd have to spend 10 minutes trying to catch her, if she knew she was going in the crate. I've also tried crating her alone a few times, and as if by miracle, nothing is shredded or soiled.
I am amazed by how far she's come....and now that she has fully realized her potential, I am delighted by what a wonderful, sweet dog she is. She is absolutely perfect. I think, given enough time, most Basenjis will make a good deal of progress. Tana was young when she was sold from the puppymill- only 1.5 years old (and already a mother). Maybe her youth helped her resiliency a little bit. But either way, adopting Tana and helping her overcome her fears has been a very rewarding experience 
